I heard something about 5-a-side games aimed at unemployed people before, but never got the details on it, sorry. Maybe it'd be worth ringing up some of the pitches around the city and asking?

I do shift work myself, so sometimes find it awkward to make it to my two regular weekly games. I know of several regular games that struggle to get players on various nights of the week. I know you said lunchtime would suit you better but maybe if you put a few feelers out you could drop in/out of some games when it suits you?